Large eddy simulation of pulsating flow over a circular cylinder at subcritical Reynolds number

The pulsating cross-flow over a single circular cylinder at the subcritical Reynolds number Re_D = 2580 is studied with the large eddy simulation (LES) technique using the standard Smagorinsky model as well as a dynamic model in which the test filtered quantities are evaluated through a truncated Taylor series expansion. The filtered equations are discretised using the finite volume method in an unstructured, collocated grid arrangement with a second-order accurate method, in both space and time. The predictions are compared against very detailed experiments for mean velocities and Reynolds stresses that were performed in a duct of cross-section 72 mm × 72 mm using the PIV technique. The effects of mesh refinement close to the cylinder as well as of subgrid scale model are also examined. The numerical predictions are in very good agreement with the measurements in terms of mean as well as turbulence quantities. The instantaneous flow patterns of the flow field are examined and the effect of the external flow pulsation on the wake characteristics such as vortex formation length, vortex strength, Strouhal number as well as the lift and drag coefficients is quantified. The vortex formation length is decreased while the mean drag, as well as the rms values of the drag and lift coefficients increase significantly under pulsating flow conditions. The performance of the LES technique is analysed in the light of the wake characteristics.     

Role of interface shape on the laminar flow through an array of superhydrophobic pillars

In this study, measurements of the pressure drop and the velocity vector fields through a regular array of superhydrophobic pillars were systematically taken to investigate the role of air–water interface shape on laminar drag reduction. A polydimethylsiloxane microfluidic channel was created with a regular array of apple-core-shaped and circular pillars bridging across the entire channel. Due to the shape and hydrophobicity of the apple-core-shaped pillars, air was trapped on the side of the pillars after filling the microchannel with water. The measurements were taken at a capillary number of Ca = 6.6 × 10^?5. The shape of the air–water interface trapped within the superhydrophobic apple-core-shaped pillars was systematically modified from concave to convex by changing the static pressure within the microchannel. The pressure drop through the microchannel containing the superhydrophobic apple-core-shaped pillars was found to be sensitive to the shape of the air–water interface. For static pressures which resulted in the apple-core-shaped superhydrophobic pillars having a circular cross section, D/D ₀ = 1, a drag reduction of 7% was measured as a result of slip along the air–water interface. At large static pressures, the interface was driven into the apple-core-shaped pillars, resulting in decrease in the effective size of the pillars and an increase in the effective spacing between pillars. When combined with a slip velocity measured to be 10% of the average velocity between the pillars, the result was a pressure drop reduction of 18% compared to the circular pillars at a non-dimensional interface diameter of D/D ₀ = 0.8. At low static pressures, the pressure drop increased significantly as the expanded air–water interface constricted flow through the array of pillars even as large interfacial slip velocity was maintained. At D/D ₀ = 1.1, for example, the pressure drop increased by 17% compared to the circular pillar. This drag increase was the result of an increased form drag due to a decrease in porosity and permeability of the pillar array and a decrease in the skin friction drag due to the presence of the air–water interface. For D/D ₀ = 1.1, the slip velocity was measured to be 45% of the average streamwise velocity between the pillars. When compared to no-slip pillars of similar shape, the drag reduction was found to increase from 6 to 9% with increasing convex curvature of the air–water interface.     

Large-eddy simulations of film cooling flows

Large-eddy simulations (LES) of a jet in a cross-flow (JICF) problem are carried out to investigate the turbulent flow structure and the vortex dynamics in gas turbine blade film cooling. A turbulent flat plate boundary layer at a Reynolds number of Re_∞ = 400,000 interacts with a jet issued from a pipe. To study the effect of the jet inclination angle α on the flow field, two angles are chosen, the perpendicular injection at 90° and the streamwise inclined injection at 30°. For the normal injection case a small blowing ratio of the jet velocity to the cross-stream velocity R = 0.1 is examined. For the streamwise inclined injection case two blowing ratios R = 0.1 and R = 0.48 are investigated to check the impact of the jet velocity on the cooling performance. The time-dependent turbulent inflow information for the cross-flow is provided by a simultaneously performed LES of a spatially developing turbulent boundary layer. Whereas in the perpendicular injection case a rather large separation region is found at the leading edge of the jet hole, in the streamwise inclined injection cases no separation is observed. Compared with the normal injection case at the same blowing ratio, the streamwise inclination weakens the jet-cross-flow interaction significantly. Thus, the first appearance of the counter-rotating vortex pair (CVP) is shifted downstream and its strength is reduced. The increase of the blowing ratio leads to a stronger penetration of the jet into the cross-flow, resulting in a more upstream located and more pronounced CVP. Downstream of the jet exit the streamwise vortices are so large that besides the jet fluid also the cross-stream is partially entrained into this zone, which yields the worst cooling performance.     

Particle mixing and reactive front motion in unsteady open shallow flow - Modelled using singular value decomposition

Passive and active tracers are used to examine particle mixing and reactive front dynamics in an open shallow flow of water past a circular cylinder. A quadtree grid based Godunov-type shallow water equation solver predicts the unsteady flow hydrodynamics of the wake behind the cylinder. The resulting periodic flow field consisting of a von Kármán vortex street is decomposed and stored over one oscillatory period using Singular Value Decomposition (SVD). Particles are advected according to the reconstructed flow field from the SVD modes, with continuous spatial velocity information obtained via bilinear interpolation. Passive particle dynamics driven by different SVD flow modes is investigated, and it is found that the flow field recovered from the mean flow and the first pair of time varying modes is adequate to represent the complicated dynamical properties induced by the original flow field. Active autocatalytic reaction, A + B → 2B, is incorporated into the particle advection model, assuming surface reaction. Active particles are found to trace out an expanded version of the unstable manifold of the chaotic saddle in the wake, in qualitative agreement with published analytical results. The numerical model is applicable to mixing and transport processes in more complicated shallow environmental flows.     

Aerodynamic drag reduction on a realistic vehicle using continuous blowing

The aerodynamic drag reduction of a realistic vehicle model through continuous blowing was numerically analyzed based on the open-source computational fluid dynamics (CFD) program, OpenFOAM. Simulations were performed on a realistic passenger vehicle model with available wind tunnel test data, DrivAer, at four different Reynolds numbers (Re). The aerodynamic drag coefficient decreased with increasing Re. The CFD technique was validated by comparing the aerodynamic drag coefficients at Re = 4.87 × 10⁶. Predicted drag coefficients of the DrivAer estate model show less than 3% difference from wind tunnel test data, whereas those of fastback and notchback vehicles showed less than 1% difference. Sectional pressure distributions agreed well with wind tunnel test data. The effect of continuous blowing was investigated using the DrivAer estate model with a blowing position at the end of the roof for vertical blowing and at the C-pillar for lateral blowing. Simulations were performed at Re = 4.87 × 10⁶ and 9.75 × 10⁶ and blowing speeds of 20%, 40%, 60%, and 100% of the vehicle driving speed. The effect of continuous blowing increased with Re. The drag reduction was more than 6% for roof blowing due to increasing rear pressure when the blowing speed equaled the vehicle driving speed. The maximum drag reduction was approximately 7.5% for simultaneous roof and lateral blowing. The results indicate that continuous blowing can efficiently reduce vehicle aerodynamic drag and consequently greenhouse gas emissions.

     

Microflow-based control of near-wall fluctuations for large viscous drag reduction

The stabilizing effect of microgroove surface morphology on viscous drag reduction was studied experimentally in the inlet region of a plane channel flow. The stabilization is thought to be due to the ability of a microgrooved surface pattern to suppress the velocity fluctuations in the spanwise direction on a restricted portion of the wetted surface, which prevents vorticity development at the wall and consequently across the entire flow field. This smart microflow control strategy, which works successfully only under very particular circumstances, was implemented in a microgroove-modified channel flow in which the front part has a microgrooved surface topology. The results of pressure drop measurements indicate that microgrooved surfaces can effectively stabilize laminar boundary layer development, leading to a significant reduction in the viscous drag. In the rear flat part of the microgroove-modified channel test section, a maximum drag reduction of DR @ 35%{\rm DR\simeq 35\%} was measured. This corresponds to an overall drag reduction of DR @ 16%{\rm DR\simeq 16\%} at a length Reynolds number of Re_x @ 10⁶.Re_x\simeq 10^6. The drag reduction effect persisted in a narrow range of flow velocities and for the reported experimental conditions corresponds to microgroove dimensions between 1.5 and 2.5 viscous length-scales.     

Flow pattern around an appended tanker hull form in simple maneuvering conditions

A detailed computational study is presented of the flow pattern around the Esso Osaka with rudder in simple maneuvering conditions: “static rudder” and “pure drift”. The objectives are: (1) apply RANS for maneuvering simulation; (2) perform verification and validation on field quantities; (3) characterize flow pattern; and (4) correlate behavior of the integral quantities with the flow field. The general-purpose code CFDSHIP-IOWA is used. The free surface is neglected and the two-equation k-ω turbulence model is used. The levels of verification of the velocity components for the “straight-ahead”, “static rudder” and “pure drift” conditions show ranges from 5.5% to 28.3% of free stream, U₀, for the axial velocity U and 2.5-29.1%U₀ for the cross flow (V, W). Qualitative validation against limited experimental data shows encouraging results with respect to trends and levels. The flow pattern is characterized by fore and aft body bilge and side vortices, which are similar for “straight-ahead” and “static rudder” conditions, except in close vicinity of the rudder. The “pure drift” condition shows strong asymmetry on windward vs. leeward sides and a more complex vortex system with additional bilge vortices. Similarities and differences with data for other tanker, container, and surface combatant hulls and relation between flow pattern and forces and moments are discussed. Future work focuses on influence of propeller.     

Surface effects on transient three-dimensional flows around rotating spheres at moderate Reynolds numbers

Transient wake flow patterns and dynamic forces acting on a rotating spherical particle with non-uniform surface blowing are studied numerically for Reynolds numbers up to 300 and dimensionless angular velocities up to Ω=1. This range of Reynolds numbers includes the three distinct wake regimes i.e., the steady axisymmetric, the steady non-symmetrical and the unsteady with vortex shedding. The Navier–Stokes equations for an incompressible viscous flow are solved by a finite volume method in a three-dimensional, time accurate manner. An interesting feature associated with particle rotation and surface blowing is that they can affect the near wake structure in such a way that unsteady three-dimensional wake flow with vortex shedding develops at lower Reynolds numbers as compared to flow over a solid sphere in the absence of these effects and thus, vortex shedding occurs even at Re=200. Global properties, such as the lift and drag coefficients, and the Strouhal number are also significantly affected. It is shown that the present data for the average lift and drag coefficients correlate well with:

C_L/(1+Ω)^3.6=0.11

C_D(1+20V_S)^0.2/(1+Ω)^Re/1000=24(1+Re^2/3/6)/Re

where V_S is the average surface blowing velocity normalized by the free stream velocity.     

Effect of tube spacing on the vortex shedding characteristics of laminar flow past an inline tube array: A numerical study

The effect of tube spacing on the vortex shedding characteristics and fluctuating forces in an inline cylinder array is studied numerically. The examined Reynolds number is 100 and the flow is laminar. The numerical methodology and the code employed to solve the Navier-Stokes and continuity equations in an unstructured finite volume grid are validated for the case of flow past two tandem cylinders at four spacings. Computations are then performed for a six-row inline tube bank for eight pitch-to-diameter ratios, s, ranging from 2.1 to 4. At the smallest spacing examined (s = 2.1) there are five stagnant and symmetric recirculation zones and weak vortex shedding activity occurs only behind the last cylinder. As s increases, the symmetry of the recirculation zones breaks leading to vortex shedding and this process progressively moves upstream, so that for s = 4 there is clear shedding from every row. For any given spacing, the shedding frequency behind each cylinder is the same. A critical spacing range between 3.0 and 3.6 is identified at which the mean drag as well as the rms lift and drag coefficients for the last three cylinders attain maximum values. Further increase to s = 4 leads to significant decrease in the force statistics and increase in the Strouhal number. It was found that at the critical spacing there is 180° phase difference in the shedding cycle between successive cylinders and the vortices travel a distance twice the tube spacing within one period of shedding.     

Melting temperature prediction by thermoelastic instability: An ab initio modelling,for periclase (MgO)

Melting temperature (T_M) is a crucial physical property of solids and plays an important role for the characterization of materials, allowing us to understand their behavior at non-ambient conditions. The present investigation aims i) to provide a physically sound basis to the estimation of T_M through a “critical temperature” (T_C), which signals the onset of thermodynamic instability due to a change of the isothermal bulk modulus from positive to negative at a given P_C-V_C-T_C point, such that (∂P/∂V)_VC,TC = -(∂²F/∂V²) _VC,TC = 0; ii) to discuss the case of periclase (MgO), for which accurate melting temperature observations as a function of pressure are available. Using first principles calculations, quasi-harmonic approximation and anharmonic correction, we model the Helmholtz potential, i.e. F(V,T), and determine pressure thereby. A comparison between measured and predicted T_M values as a function of pressure shows achievement of an average discrepancy of ~2.9%, in the range 0–25 GPa and 3000–5000 K.     

A numerical study of flow past a cylinder with cross flow and inline oscillation

Two-dimensional fluid flow around an oscillating circular cylinder is studied numerically at different values of oscillation frequency and amplitude. A novel finite element method which uses discretization along the characteristic line is used for simulation. The solver is coupled to a mesh movement scheme using the Arbitrary Lagrangian-Eulerian (ALE) formulation to account for body motion in the flow field. Two cases of cylinder motion have been studied, cross flow and inline oscillation. In both cases, occurrence of lock on is investigated and the bounds of the lock on region are determined. A comparison of the numerical results with the experimental data indicates that 2D simulation is valid up to Re = 300. Beyond that, 3D effects appear. By using flow visualization, effect of a cylinder oscillation on the flow field and wake pattern has been studied. Also, variation of the mean drag coefficient against the oscillation parameters is discussed. The numerical results are in good agreement with the experimental data available in the literature.     

Instability of the flow in the vicinity of trailing edge of a class of thin aerofoils

A numerical study has been undertaken to investigate the notion of absolute/convective instability in laminar incompressible trailing edge flows past wedge-like shapes with curved boundaries of the form y=α(−x)^m. The effects of various trailing edge shapes m and relative thickness α on the flow separation and the development of instabilities in the vicinity of trailing edge are investigated. The nonlinear viscous-inviscid interaction equations, which have been derived by means of the asymptotic theory of flow separation, are solved first numerically to construct genuine mean velocity profiles representing the correct flow in the vicinity of the trailing edge. The absolute/convective nature of the asymptotically formed velocity profiles via a composite expansion is then ascertained by using a spatio-temporal analysis based on the Briggs-Bers pinching criterion. Although no absolute growth is encountered upstream of the trailing edge of the airfoil shapes considered, in particular the wake region behind the trailing edge of Joukowski type profiles is found to be persistently susceptible to absolute instability. It is found that separation is enhanced as the relative thickness of the airfoil gets bigger. This, in turn, is shown to lead to an additional enhancement of the absolute instability character by both increasing the absolute growth rate as well as the extent of the unstable region. Shedding frequency of the Karman vortex street is also determined behind the trailing edge shapes considered.     

Control of flow using genetic algorithm for a circular cylinder executing rotary oscillation

We propose here a new approach to optimally control incompressible viscous flow past a circular cylinder for drag minimization by rotary oscillation. The flow at Re = 15000 is simulated by solving 2D Navier-Stokes equations in stream function-vorticity formulation. High accuracy compact scheme for space discretization and four stage Runge-Kutta scheme for time integration makes such simulation possible. While numerical solution for this flow field has been reported using a fast viscous-vortex method, to our knowledge, this has not been done at such a high Reynolds number by computing the Navier-Stokes equation before. The importance of scale resolution, aliasing problem and preservation of physical dispersion relation for such vortical flows of the used high accuracy schemes [Sengupta TK. Fundamentals of computational fluid dynamics. Hyderabad, India: University Press; 2004] is highlighted.For the dynamic problem, a novel genetic algorithm (GA) based optimization technique has been adopted, where solutions of Navier-Stokes equations are obtained using small time-horizons at every step of the optimization process, called a GA generation. Then the objective functions is evaluated that is followed by GA determined improvement of the decision variables. This procedure of time advancement can also be adopted to control such flows experimentally, as one obtains time-accurate solution of the Navier-Stokes equation subject to discrete changes of decision variables. The objective function - the time-averaged drag - is optimized using a real-coded genetic algorithm [Deb K. Multi-objective optimization using evolutionary algorithms. Chichester, UK: Wiley; 2001] for the two decision variables, the maximum rotation rate and the forcing frequency of the rotary oscillation. Various approaches to optimal decision variables have been explored for the purpose of drag reduction and the collection of results are self-consistent and furthermore match well with the experimental values reported in [Tokumaru PT, Dimotakis PE. Rotary oscillation control of a cylinder wake. J Fluid Mech 1991;224:77].     

Biased scan of plasma display panel for data voltage reduction

This paper proposes a method of reducing the data voltage V_d of plasma display panels (PDPs). The proposed biased-scan method uses two separate ground systems: one for the sustain pulse generator (FGND) and the other for the data address and control systems (CHGND). A dc voltage bias, which is applied between CHGND and FGND during the address period, reduces V_d while preventing the undesired glow discharge induced by a scan pulse only. CHGND is connected to FGND for the first sustain pulse of each subfield, which reduces the time lag of address discharge, but it is separated from FGND for the other sustain pulses to increase the margin of the sustain voltage. The proposed method was tested on a 15% Xe 50-in. Full HD (1920 × 1080) single-scan PDP which had a sustain discharge gap of 110 μm. V_d could be reduced by 20 V (30%), and the power consumption of the V_d voltage source decreased by ∼25 W (50%) from that of the conventional method.     

Numerical simulation of an oscillating cylinder in a cross-flow at low Reynolds number: Forced and free oscillations

A numerical simulation of the flow past a circular cylinder which is able to oscillate transversely to the incident stream is presented in this paper for a fixed Reynolds number equal to 100. The 2D Navier-Stokes equations are solved by a finite volume method with an industrial CFD code in which a coupling procedure has been implemented in order to obtain the cylinder displacement. A preliminary work is first conducted for a fixed cylinder to check the wake characteristics for Reynolds numbers smaller than 150 in the laminar regime. The Strouhal frequency f_S and the aerodynamic coefficients are thus controlled among other parameters. Simulations are then performed with forced oscillations characterized by the frequency ratio F = f₀/f_S, where f₀ is the forced oscillation frequency, and by the adimensional amplitude A. The wake characteristics are analyzed using the time series of the fluctuating aerodynamic coefficients and their power spectral densities (PSD). The frequency content is then linked to the shape of the phase portraits and to the vortex shedding mode. By choosing interesting couples (A, F), different vortex shedding modes have been observed, which are similar to those of the Williamson-Roshko map. A second batch of simulations involving free vibrations (so-called vortex-induced vibrations or VIV) is finally carried out. Oscillations of the cylinder are now directly induced by the vortex shedding process in the wake and therefore, the time integration of the motion is realized by an explicit staggered algorithm which provides the cylinder displacement according to the aerodynamic charges exerted on the cylinder wall. Amplitude and frequency response of the cylinder are thus investigated over a wide range of reduced velocities to observe the different phenomena at stake. In particular, the vortex shedding modes have also been related to the frequency response observed and our results at Re = 100 show a very good agreement with other studies using different numerical approaches.     

Flow characteristics of two rotating side-by-side circular cylinder

This paper presents a numerical investigation of the characteristics of the two-dimensional laminar flow around two rotating circular cylinders in side-by-side arrangements. In order to consider the combined effects of the rotation and the spacing between two cylinders on the flow, numerical simulations are performed at a various range of absolute rotational speeds (|α|?2) for four different gap spacings of 3, 1.5, 0.7 and 0.2 at Reynolds number of 100 showing the typical two-dimensional vortex shedding. As |α| increases, the flow changes its condition from periodic to steady after a critical rotational speed, which depends on the gap spacing. In the cases of gap spacings of 3 and 0.2, the wake keeps the same pattern, until flow reaches the steady state. However, for the gap spacings of 1.5 and 0.7, the wake patterns change in the unsteady regimes. For the cases in which the flow is unsteady, the Strouhal number strongly depends on the gap. For a fixed gap spacing, the variation of the Strouhal number is significant when the wake pattern is changed according to the rotational speed. Regardless of the gap spacing, as |α| increases, the lift increases and the drag decreases. Quantitative information about the flow variables such as the pressure coefficient and wall vorticity distributions on the cylinders is highlighted.     

Computations of optimal cylinder flow control in weakly conductive fluids

A nonlinear adjoint-based optimal control approach of cylinder wake by electromagnetic force has been investigated numerically in the paper. A cost functional representing the balance of the regulated quantities with different weights and interaction parameter N (Lorentz force) has been constituted, where the regulated quantities related with flow and force are taken as targets of regulation and the Lorentz force, (as interaction parameter N), is taken as a control input. Based on the cost functional and Navier-Stokes equations, the corresponding adjoint equations have been derived and the sensitivity of the cost functional is found to be a simple function of the adjoint stream function in the adjoint field. For the different regulations, the forms of optimal control rules are similar while the adjoint equations are different. The receding-horizon predictive control setting is employed to discuss the optimal control problems. Under the action of optimal N(t), the flow separation is suppressed fully, so that the oscillations of drag and lift are suppressed and the total drag coefficient decreases dramatically. For the different regulations, the control effects have some differences due to the different values of optimal inputs corresponding to the different adjoint flow fields.     

Study of CFD variation on transport configurations from the second drag-prediction workshop

This paper describes and analyzes a series of nearly 90 CFD test cases performed as a contribution to the second Drag Prediction Workshop, held in Orlando, Florida in June 2003. Two configurations are included: DLR-F6 wing-body and wing-body-nacelle-pylon. The ability of CFD to predict the drag, lift, and pitching moment from experiment--including the “delta” arising from the addition of the nacelle and pylon--is assessed. In general, at a fixed angle of attack CFD overpredicts lift, but predicts the ΔC_L reasonably well. At low lift levels (C_L < 0.3), ΔC_D is 20-30 drag counts (30-45%) high. At the target lift coefficient of C_L  =  0.5, ΔC_D is overpredicted by between 11 and 16 counts. However, the primary contribution of this paper is not so much the assessment of CFD against experiment, but rather a detailed assessment and analysis of CFD variation. The series of test cases are designed to determine the sensitivity/variability of CFD to a variety of factors, including grid, turbulence model, transition, code, and viscous model. Using medium-level grids (6-11 million points) at the target lift coefficient, the maximum variation in drag due to different grids is 5-11 drag counts, due to code is 5-10 counts, due to turbulence model is 7-15 counts, due to transition is 10-11 counts, and due to viscous model is 4-5 counts. Other specific variations are described in the paper.     

On the convergence of the bilinear-velocity constant-pressure finite element method in viscous flow

In this paper we show that the standard isoparametric Q₁ × Q₀ velocity pressure finite element method for solving viscous flow problems leads to a fully and optimally convergent sequence of approximations, if an appropriate quadrangulation of the domain is used.     

Simulation of fish swimming and manoeuvring by an SVD-GFD method on a hybrid meshfree-Cartesian grid

In this paper we present the development of the Singular-Value Decomposition (SVD) based Generalized Finite Difference (GFD) method for the simulation of fluid-structure interaction (FSI) problems in a viscous fluid. The class of FSI problems is exemplified by the self-propulsion (swimming) and dynamic manoeuvring of deforming (undulating and flexing) bodies in a fluid medium. Computation is carried out on a hybrid grid comprising meshfree nodes around the undulating swimming body and Cartesian nodes in the background. The meshfree nodes are convected in tandem with the changing shape and motion of the swimming body. The resultant locomotion of the swimmer is governed by fully-coupled dynamic interaction between the deforming body and the fluid in accordance with Newton’s laws. Time integration of motion is carried out by a Crank-Nicolson based implicit iterative algorithm, which fully couples the changing position of the swimming body with the evolving flow field, for numerical stability. The numerical scheme is applied to the steady swimming/cruising and sharp turning manoeuvres of a two-dimensional carangiform fish. The Strouhal number approaches values for efficient steady swimming reported in Fish and Lauder (2006) and Triantafyllou and Triantafyllou (1993) [3] and [6] at high Reynolds number. An illustrative example shows the numerical carangiform swimmer executing a sharp turn through an angle of 70° from straight coasting within a space of about one body length. The results obtained are consistent with available literature. In steady swimming, the momentumless wake theoretically anticipated by Wu (2001) [57] is successfully reproduced here, as opposed to the inverse von Karman vortex street generally predicted by inviscid flow models. The momentumless wake, characterized by an aligned series of alternately-signed shed vortices, is symptomatic of a state of average equilibrium between drag acting on the body of the fish and thrust produced by its undulating tail fin. Guided swimming towards targets based on a simple feedback control scheme is also demonstrated.